For example, there have been concerns raised about whether the U.S. should continue to support the U.N., said Jon Condra, director of East Asian research and analysis at Flashpoint.

"If these kinds of organizations start breaking down or lose credibility, we're going to be in a place where it's going to be a lot harder to come to some sort of agreement," he said. "Pulling away from international institutions that are designed to come to a consensus on major issues of international importance would have an impact."

It's the wrong time to try to make progress, said Anup Ghosh, founder and CEO at security firm Invincea.

Ghosh is a former offensive researcher with the Department of Defense, and points to the recent attempts to restrict international travel as one example of potential problems.

"The more we constrict and insulate ourselves from the world, the less likely our allies are going to cooperate from us, including on things like law enforcement actions," he said. "Most of the cyber criminals that we try to chase down have been protected by Russia. Today, we typically get them when they travel abroad on vacation."

On the other hand, he added, if cooperation with Russia does improve, then extradition could become easier.

Or not.

According to Flashpoint's James, Russia has a different approach to cybercrime than the West does.

"They don't look at it as crime, they look at it as business," he said. "It's not about them getting their act together. From their point of view, they have their act together."

"In the current geopolitical environment, it seems really unlikely that the Russian and Chinese governments will be willing to cooperate on cybercrime investigations where the primary suspect is in China or Russia," said Levi Gundert, vice president of threat intel at security firm Recorded Future.

Gundert previously worked for the U.S. Secret Service, and has also observed the important role that personal relationships play in international law enforcement efforts.

"You'd go to a conference, sit down with officials from other countries, drink some vodka, eat some cold cuts, and form these relationships of trust," he said. "And that's how some of the bigger cybercriminal cases happened. It may not be through official channels, but there's a lot of cooperation that happens to get cases done."

Even when, say, Russia is unwilling to extradite a cybercriminal, good relationships with other countries can help.

"There have been lots of high-profile cases of extradition from the Maldives and France and other countries where Russians tend to vacation," he said. "That's been very successful. When you can hamper these peoples' ability to travel, it affects them."